MancJiestcr Memoirs, Vol. xliv. (1899), No. 5. 19 



It may be well to recall that U represents the velocity 

 at which a weight equal to W would have to be raised in 

 order to do work equal to that done by the propellinc,^ 

 force F. By (20), caeteris paribus., f/ varies as S~\ 



We may now pass to the case of an aeroplane gliding 

 in still air, the path being slightly inclined downwards. 

 If (^ be the small angle between the path and the hori- 

 zontal, we may regard the component of gravity in this 

 direction, viz., Jf'sinO, as the propelling force F. Thus 



71= JVU == FV = JVVsind . . . (22), 

 so that 



l7=Fsmd (23). 



The same equations apply as before, with the under- 

 standing that a, being the inclination of the plane to the 

 direction of motion through the air, is no longer identical 

 with the inclination of the plane to the horizon. The 

 latter angle, reckoned positive when the leading edge is 

 downwards, will now be denoted by (6 — a). 



Introducing (23) into (14), (15), we get 



V~= o ■ ^ ' sina = . . . . (24), 



kS sin d IV ^ 



from which it appears that whatever may be the values of 

 U^ and S, may still be as small as we please. Thus, if 

 frictional forces can be neglected, a high speed is all that 

 is required in order to glide without loss of energy. This 

 is the supposition upon which we discussed the manner in 

 which a bird may take advantage of the internal work of 

 the wind ; and we see that the motion of the bird must 

 be of such a character that he alwaj's retains a high 

 velocity relatively to the surrounding air. The advantage 

 that we showed to be obtainable must be set against 

 losses due to friction and to imperfect fulfilment of the 

 condition just specified. 



